White, J.H., and W.R. Bauer, 1986, "Calculation of the twist and the writhe forrepresentative models of DNA," Journal of Molecular Biology 189, 329-341.

two distant segmentsofa DNA axisare brought very close together, then this proximity will contributeapproximately±1to the writhing number because in almost all viewsthis proximity will be seen as a crossing.

writhing numberisdefined as the average over all possible viewsofthe projected writhing number

helical windingofthe backbone curve around theaxis

DNA axis is seen to cross itself,

writheWrand twist Tw,which can be used to describe supercoiling (White, 1969)

For a relaxed circular DNA moleculeofthe monkey virus SV40,which has approximately 5,250 base pairs,Lkis about 500, and forbacteriophage Aofabout 48,510 base pairs,Lkis about 4,620

does not depend on theprojection or viewofthe pair

one adds allofthe signed numbers associated with thisprojection and divides by 2, one obtains the linking numberofthe curvesA and C,Lk(A,C)

Such a viewgives a modified projectionofthe pairofcurve

topologyofknot theory to explain the actionofenzymes in carrying out the fundamental processofsite-specificrecombination.

supercoiling helps incellular packaging of DNA in structures called nucleosomes, in whichDNA is wound around proteins called histones

cruciforms

polyrnerases

helicases

Supercoiling of closed DNA is ubiquitous in biological systems

may, in general, assume almostany configuration in space

xis ofthe double helix may itself be a helix

commonlinear axis

fundamental theorem

ormula for the sum ofthe first a + 1 terms of a geometric series with ratio p

Since the arithmetic function f(d) = d is multiplicative (verifythis!), we have that u(n) is multiplicative by Theorem 3.1

disjointness of sub-graphs in G′ ensures that these paths do not cycle

each node in the coregraph has degree either zero or two

ode has two incident edges

node is isolated in G′ and has degree zero

e1, e2, e3,and e4 belong in E

edge to belong in E′only if it lies between a X-face and an O-face

If every tile of the Hex board is markedeither x or o

u and v now have degree at most 1 since they had degree atmost two before we removed edge (u, v)

all the nodes are isolated

Each node can have degree at most two, so g can haveat most N edge

Figure 18

return to itsnatural twist rate,

Lk(R) = T w(R) + W r(R).

linking number of the ribbon is equal to the linkingnumber of this link

average signed crossover number over all possible projections of the ribbon inspace

Definition 2.3

duplex DNA

tangles

S = (-3, 0)and R = (1)

substrate molecule as N (S + T ) and the product molecule as N (S + R)

knot Q

substrate molecule (the molecule before the enzyme acts)

circular (cyclic) DNA

several more general action

projections

measure of howintertwined two components of a link are

linking number

new terminol-ogy, writhe, to model this type of cyclic DNA.

examples of your ow

explanations of proof ideas or important results if relevant

10access to the shared resources. In addition, it only considers a singleprocessor and ignores the overhead caused in changing the mode. In thefuture, we will focus on scheduling energy aware dependent periodictasks in multiprocessor MC real-time systems with the overhead ofchanging the mode

reduce energy consumption up to 32.45 and46.84% compared with Algorithm A in the normal mode and urgencymode, respectively

Effect of the ratio of Ci (LO)Ai (L

energy consumption up to 32.45% in the urgency mode

herefore, EAU can reduce energy consumption up to41.63%

can reduce energy consumption up to 21.17%

normalized energy consumption when ULOLO(Γ) was equal to 0.45

In addition, the ratio of Ci(LO) and Ai(LO) was set to 5 for any task τi.

1.3

ULOHI (Γ)

Effect of UHIHI (Γ)

Therefore, EAU can reduce energy consumption up to 46.30% inthe urgency mode compared with Algorithm A as shown in Fig. 9(b).

actualexecution time of tasks

pplied the uniform distribution method to select theparameter of the task

slack time generated from the early completion jobs and the jobswere executed with Shigh in the urgency mode.

HI level task is executed with Smax in the urgencymode

rocessor could providediscrete normalized speed levels, i.e., [0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9,1.0]

That is Pind = 0.1, Pmaxdynamic was normalized to 1 and θwas set to 0.2 in Eq. (1) [2]

Pind = 0.1, Pmaxdynamic = 1 and θ = 0.2

Case 3: EAU is feasible in a changed mode

sum utilization of tasks

asks are put intothe delay queue

other is a delay queue that in-cludes the unreleased and completed job

If the HI level job τijends and its execution time exceeds Ci(LO)/S under S, the system willswitch to the urgency mode

Smax

Algorithm A computes the parameter x= 0.875, the optimal speed of LO tasks SLO = 0.86, and the optimal speedof HI tasks SHI = 0.90

Ci(LO) ≤ Ai(HI)

When the HI level task is not completed on time and its execution timeexceeds the worst case execution time (WCET) in the normal modeunder the processor speed S

If ζ = LO, then the virtual deadline of τi is assigned to ti + T

within the time not exceeding Ci(LO)/S

execution of any task τi is completed under S

apply the utilization analysis method to prove that EAU isfeasible.

power-awar

optimal speed iscomputed to reduce energy consumption in the normal mode

switches to the urgency mode inwhich only HI level tasks can be executed.

MC system is driven by the power, cost, area andweight

focus on the actualexecution time of task

Wederived the energy model parameters from the state-of-the-art researches in this area [24], [28], [29], [37], [38]. Weassumed thatmaxdynamicP is normalized to 1 and0.1

Static and dynamicpower components can be reduced by selecting lowerivalues for a task

)dynamicmaxi ind i i

I

P

P

optimal x is 0.625 where f HIand f LO are 0.7 and 0.5 in each

urrently-executing job executes for more than itsLO -criticality WCET without signaling completion

ob is assigned a scheduling deadlineequal to t + ˆTi

lies somewhere within the interval

x U LOLO (τ ) + U HIHI (τ ) ≤ 1

sufficientcondition for ensuring that EDF-VD successfully meets allHI -criticality deadlines during all HI -criticality behaviors ofτ

x ← U LOHI (τ )1 − U LOLO (τ )

ll currently-active LO -criticality jobs are immediately dis-carded; henceforth, no LO -criticality job will receive anyexecution

ta + ˆTi

ta + Ti

Ti ≤ Ti

τ

U yx (τ ) =∑τi ∈τ ∧χi =xCi(y)Ti

all HI -criticality jobs receive enough execution between their releasetime and deadline to be able to signal completion.

Each such job has a deadline that is Tk time unitsafter its release.

erroneous behavior

if evenone job Ji signals completion after executing for more thanci(LO) but no more than ci(HI) units of execution, we saythat the system has exhibited HI-criticality behavio

γi

sporadic

run-timecomplexity per scheduling decision was logarithmic in thenumber of task

[8]

Integrated Modular Avion-ics (IMA) [19] in aerospace and AUTOSAR

Mawhin, J. (2007). Le th ́eor`eme du point fixe de Brouwer: un si`ecle de m ́etamorphoses.Sciences ettechniques en perspective10(2): 175–220.

nteresting trade-offbetween energy efficiency and system reliability

static power, which includes the power tomaintain basic circuits and keep the clock running.

reduces supplyvoltage for lower frequency requirement

CMOS

with υn = 0

Utot denotes the total utilization of the task set

Di ≤ Ti

Qi

q D 1

Formally, if L, L1 , and L2are languages on 

Whenever a tableau is infeasible wewill say that we are in Phase I of the Simplex Algorithm; Phase II ifPhase I/IIthe tableau is feasible

Workout 21

Workout 20

Workout 19.

Workout 15

Prove

Design

b

a

counterexample

For

Stable Matching

Multiple slots

Workout 22

Workout 17

Workout 16

Geometric Introduction: Week 2

Hipster Coffee Tours

My algorithm is Ω(1)

Banana’s algorithm is Ω(n3), so you should be careful.

prove the statement by induction

The number of pairs of pointsis (n2) = n(n−1)2 , and since this quantity is bounded by 12 n2

For a woman w, we need to decide if w is currently engaged, and if sheis, we need to identify her current partner

We need, for a man m, to be able to identify the highest-ranked womanto whom he has not yet proposed

We need to be able to identify a free man.

we will only need to use twoof the simplest data structures: lists and arrays

suppose, by way of contradiction

favoringmen

accepting those that increase the rank of her partner

Inequality 1.4.7

Workout 1.2.6

Tier A Standards

depicted Ellis Act evictionsthrough a series of “explosions” in which red dots eruptacross the city, corresponding to the number of unitsevicted (as filed with the San Francisco Rent Board).The map provided a quantitative yet visceral geo-graphic representation of displacement in the city, thered eviction dots leaving the city pockmarked andblemished by the end of the time lapse.

The Anti-Eviction Mapping Project: CounterMapping and Oral History toward Bay AreaHousing Justice

mongthespectralcolors,NorthAmericanadultsseemtopreferblueandredtogreenandviolet,andgreenandviolettoorangeandyellow.Leas

oolchildrenlikehighlysaturatedcolors,suchasbrightred,green,andblu

useofspectralhuestoportrayintensitydifferencesisastrongcluethatthemapmakereitherknowslittleaboutmapdesignorcareslittleaboutthemapuser

espreadignoranceofhowcolorcanhelporhurtamap.Personsunawareoftheappropriateuseofcolorincartographyareeasilyimpressedandmightacceptasusefulapoormapthatmerelylookspretty.

xtremelyhighorextremelylowvaluesisolat

Areareallyaggregateddatabad?Sur

In the course of m y research, 1 ha ve thought of literary maps as good tools to analyze plot, but not much else, and certainly not style

Readers needed a symbolic form capable of making sense of the nation-state

reiterated Ínter-play defines the nation as the su m of all its possible stories

Are there, in other words, events that · tend to happen in real spaces- and others that 'prefer' fictional ones? It is early to give a definitive answer, but Austen's novels certainly suggest that fictional spaces are particu-larly suited to happy endings, and the wish-fulfillment they usual! y embody. By contrast, the more pessimistic a narrative structure becomes, the more infrequent are its imaginary spaces.

an asymmetry of the real and the i.maginary- of geography, and litera-ture- that will recur throughout the present research

strange, harsh novelty of the modern state-and turn it into a large, exquisite home.

Austen's novelistic geography shows all its intelli-gence.

potential' .states, 1 would say, rather than actual ones.

nation-state ... found the novel. And viceversa: the novel found the nation-state. And being the only symbolic form that could represent it, it became an essential component of our modern culture.

between the novel and the geo-political reality of the nation-state

In the hope that the visual construct will be more than the su m of its parts: that it will show a shape, a pat-tern that may add something to the information that went into makingit.

adjective that I had never dreamt of applying to myse

ilaps play in them a wholly peripheral role. Decorative.

points of departure, then: for m y reflections

ortgebunden

ghost

Probably the best place to read tacos on campus

The fi replace isn’t real but if you close your eyes really tight and think about Bambi fl eeing a forest fi re you can almost smell smoke

reehouse of Sighs.

Offi ce of Incandescent Light and Industrial Runoff.

still feel a thrill when my location on Earth is validated by satellites in space.

My GPS told me my worth. It told me my place in the universe.

military intentionally reduced the system’s accuracy for everyone else under a program called Selective Availability.

Spiritual validation: the satellite gods in the sky have deemed me to be exactly where I think I am.

The fi gure on the screen roughly corresponded to my independent estimate,” Jack says with wonder. An “estimate,” he continues, “feebly arrived at after long searches through documents, tormented arithmetic. Waves of relief and gratitude fl owed over me. The system had blessed my life. I felt its support and approval.

I don’t want to know to where I’m going or how to get there. I want to know where I am.

I am strangely drawn to the power of GPS, to the possibility of knowing my precise location on the face of the planet.

These counter-sites are juxtaposed against one another, often telling very different stories about the same location

Michel Foucault,

A game in which teams work to leave fragments of a narrative around various spaces using existing locative social media.

Mark Sample

CIA pocket atlas used by American foreign service personnel has a detailed, fully indexed, eas